Romantic, matching masterpieces of mid-20th century air travel touched down this week in John F. Kennedy Airport’s otherwise charmless heart. One has wings, the other merely seems eager to fly. Both are tickets back in time to the golden age of slow-paced luxury at 35,000 feet.

The Eero Saarinen-designed TWA flight terminal, dark since 2001, has been transformed into an eats- and booze-rich lobby in the 512-room TWA Hotel set inside two new buildings at either end of the terminal.

Outside gleams a restored TWA Constellation, perhaps the prettiest plane ever to fly, now turned into a glam cocktail lounge. The twin projects, which cost developer MCR $265 million to design, could actually make the widely hated airport less hated.

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The eye-popping concrete-and-glass terminal today looks exactly as it did 57 years ago — “one of the great masterpieces of expressionistic modern design,” as the Landmarks Preservation Commission called it.

Saarinen, with collaborator Kevin Roche, said that he wanted to “interpret the sensation of flying” with swooping concrete walls, snaking staircases and mezzanines, ceiling vaults and vast windows to let in the sky. Its floor was made of 396,000 white “penny tiles,” its carpets and upholstery a vivid chili-pepper red.

The terminal’s 200,000 square feet — “the largest hotel lobby in the world,” developer Tyler Morse says — lie beneath a concrete roof that’s supported by just four columns, an engineering marvel in the pre-computer age.

Yet, it was “functionally obsolete the day it opened” in 1962, says project mastermind Morse, the CEO and managing partner of MCR. Although often called an “icon of the jet age,” he says, it was actually designed not for jets, but for old-school propeller planes.

Visitors take in the vibrant red Sunken Lounge.Annie Wermiel/NY Post

When TWA owner Howard Hughes launched the terminal project in 1956, the four-prop Constellation was the queen of the air. Its dolphin-shaped fuselage and distinctive, three-fin tail made it sleeker and sexier than its main competitor, Pan Am’s tubby Boeing Stratocruiser.

But while the Constellation carried 50 well-heeled passengers, the Boeing 707 jetliner, launched in 1958, carried twice as many — at twice the speed of “Connie’s” plodding 300 mph.

The terminal could barely handle the heavier traffic, much less that of the jumbo 747 that first flew in 1969. Even so, TWA continued to use it until the airline shut down in 2001.

Under the watchful eye of 22 government agencies, preservation specialists Beyer Blinder Belle restored the terminal to its original glory. Except for a few, 21st century grab-and-go food outlets (such as the Halal Guys and Empanada Republic) cleverly set up at onetime airline check-in counters, it’s a full-blown fantasy of Eisenhower- and JFK-era air travel, replete with original clocks, crew uniforms and a flip-panel arrivals and departures board. (How long did TWA’s lumbering prop planes take to reach Kinshasa in the former Belgian Congo?)

An original clock (left) graces the restoration. A robe and other amenities (right) await guests in a hotel room.Annie Wermiel/NY Post

TWA ticket counters became check-in desks for the hotel, which was designed by Lubrano Ciavarra Architects. Jetway corridors that led to departure gates now take hotel guests to rooms accessorized with rotary telephones and vintage magazines.

Superchef Jean-Georges Vongerichten runs a precise replica of the terminal’s original, mezzanine-level Paris Café (salads and pizza under $20, a $26 cheddar burger and mains such as $32 seared salmon). The Gerber Group nightlife experts handle boozing venues including the terminal’s bright-red Sunken Lounge, a lounge inside the Constellation, and another on the hotel roof which will have a year-round infinity pool and observation deck. They feature 1950s aviation-themed cocktails, most $16, including the Come Fly With Me (vodka, St. Germain, prosecco and lime).

The red-and-white Lockheed Constellation is an instant-smiles machine. Visitors to the earthbound beauty, which only fits 30 at a time, can sit on plush, original seats or stools for cocktails served from a rear bar by hostesses in vintage uniforms, and drop into the evocatively restored cockpit.

A variety of vintage uniforms are on display.Annie Wermiel/NY Post

This particular plane joined TWA’s fleet in 1958, when passengers enjoyed two-by-two seating in a wide-body cabin that’s unimaginably spacious, even by today’s first-class standards. But with the 707’s advent, TWA demoted the plane to cargo duty after just two years.

It was sold for Alaskan cargo lifts and later went through unglamorous decades of bargain-basement auction sales and repossession by the Feds. Morse picked it up from the most recent previous owner, Lufthansa, 18 months ago.

The beauty’s saddest period came when new owners adapted it for South- and Central American marijuana drops from 1973-83.

“The drug merchants added a big cargo door at the rear to forklift weed,” Morse chuckled. “It makes it much easier to get food and beverage in today.”

The TWA Constellation plane has been transformed into the glam Connie cocktail lounge.Annie Wermiel/NY Post

If you go …

The TWA Hotel terminal is open to the public 24/7. It can be reached most easily by car or AirTrain to Terminal 5.

Reservations for the TWA Hotel can be made only via TWAHotel.com/rooms. Bookings are taken for overnight and also for daytime stays (morning until early evening).

You don’t need to be a hotel guest to use the restaurants and lounges, but don’t schlep to JFK without making reservations first. Paris Café bookings can be made at Resy.com.

Reservations for the Gerber Group venues (Sunken Lounge, Connie lounge (that’s the plane), etc., can be made on SevenRooms.com.

The Connie cocktail lounge is a rechristened TWA plane originally called the Constellation.

Annie Wermiel/NY Post

Guests inquire about checking in at the hotel.

Annie Wermiel/NY Post

A rooftop infinity pool and lounge offers ample opportunity to check out airplane arrivals and departures.